Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2 + 14}{x - 7} = \dfrac{30}{x - 7}$
Explanation: Multiply both sides by $x - 7$ $ \dfrac{x^2 + 14}{x - 7} (x - 7) = \dfrac{30}{x - 7} (x - 7)$ $ x^2 + 14 = 30$ Subtract $30$ from both sides: $ x^2 + 14 - (30) = 30 - (30)$ $ x^2 + 14 - 30 = 0$ $ x^2 - 16 = 0$ Factor the expression: $ (x + 4)(x - 4) = 0$ Therefore $x = -4$ or $x = 4$